See my edit above we were typing at the same time. When there is no pricing mechanism more is always better.
There is no evidence of over-use, only of high prices. See my link above, the US uses health care at comparable rates to other countries that are much less expensive. There is also basically no system on earth where the government pays everything and the research shows that modest copays are excellent at controlling unnecessary usage. (along with physician controls of those things)
This is the free market two-step you're trying to engage in:
1) due to lack of government regulation health care is extremely expensive in the US as compared to other countries.
2) to solve this problem we should make consumers bear more of the inflated health care costs the free market has produced. When they simply elect no longer to get the medical care they need that means the free market has reduced costs!!
Wouldn't the more logical step be to implement the government regulations other countries have which have successfully controlled costs, then we can just have the same care for less money?